轉動機械系統之階次分析

Abstract

本研究的主要目標是希望研究發展一套針對多轉軸之轉動機械的階次方法，以更有效地來監測轉動機械。在傳統的階次分析法上，是以傅立葉分析法為主，並配合軸的轉速來達到轉動機械的階次追蹤(Order Tracking)。然而在轉軸轉速變化的情形下，再取樣過程(Resampling)常被用於取捨時、頻域上的解析度。此方法有許多缺點，尤其是相鄰近階次與相交越階次上，存在有頻率抹平(Frequency Smearing)的現象，而且傳統的階次分析法也無法處理多轉軸機械系統。在本文中將提出兩種適應性階次追蹤技術(Adaptive Order Tracking Technique)，分別利用遞迴式最小平方法(Recursive Least-Squares method)與卡氏濾波器(Kalman Filter)，來解決傳統的階次分析法所遇到的困難。研究內容主要包含兩個方面：第一，傳統方法與新方法的理論架構陳述；第二，針對實務上所可能遇到的條件因子，進行不同組合的電腦數值模擬、測試，並根據模擬結果進行討論。

The aim of this research is to develop an order tracking method for monitoring and diagnosis of any multi-rotating axle machinery. Conventional methods of order tracking are primarily based on Fourier analysis with reference to shaft speed. Resampling process is generally required in the fast Fourier transform (FFT)-based methods to compromise between time and frequency resolution for various shaft speeds. Conventional methods suffer from a number of shortcomings. In particular, smearing problem arises when closely spaced orders or crossing orders are present. Conventional methods also are ineffective for the applications involving multiple independent shaft speeds. This paper presents two adaptive order tracking techniques based on Recursive Least-Squares (RLS) filtering and Kalman filtering to overcome the problems encountered in conventional methods. The work includes two major parts. The first part is the theoretical background of conventional methods and the proposed methods. In the second part, we verify the proposed methods and discuss the results by using computational numerical simulations.